Integro-Differential Boundary Conditions to the Sequential ?1-Hilfer and ?2-Caputo Fractional Differential Equations

In this paper, we introduce and study a new class of boundary value problems, consisting mixed-type ?1-Hilfer ?2-Caputo fractional order differential equation supplemented with integro-differential nonlocal conditions. The uniqueness solutions is achieved via the Banach contraction principle, while existence results established by using Leray–Schauder nonlinear alternative. Numerical examples are constructed illustrating obtained results.